Asymptotic Results for Multinomial Models

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have no...

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Autores principales:	Isaac Akoto, João T. Mexia, Filipe J. Marques
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	confidence ellipsoids covariance matrices limit distributions classification non-linear models Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/80aa35ec2de34cefab15287604734821
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spelling	oai:doaj.org-article:80aa35ec2de34cefab152876047348212021-11-25T19:07:20ZAsymptotic Results for Multinomial Models10.3390/sym131121732073-8994https://doaj.org/article/80aa35ec2de34cefab152876047348212021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2173https://doaj.org/toc/2073-8994In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.Isaac AkotoJoão T. MexiaFilipe J. MarquesMDPI AGarticleconfidence ellipsoidscovariance matriceslimit distributionsclassificationnon-linear modelsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2173, p 2173 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	confidence ellipsoids covariance matrices limit distributions classification non-linear models Mathematics QA1-939
spellingShingle	confidence ellipsoids covariance matrices limit distributions classification non-linear models Mathematics QA1-939 Isaac Akoto João T. Mexia Filipe J. Marques Asymptotic Results for Multinomial Models
description	In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.
format	article
author	Isaac Akoto João T. Mexia Filipe J. Marques
author_facet	Isaac Akoto João T. Mexia Filipe J. Marques
author_sort	Isaac Akoto
title	Asymptotic Results for Multinomial Models
title_short	Asymptotic Results for Multinomial Models
title_full	Asymptotic Results for Multinomial Models
title_fullStr	Asymptotic Results for Multinomial Models
title_full_unstemmed	Asymptotic Results for Multinomial Models
title_sort	asymptotic results for multinomial models
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/80aa35ec2de34cefab15287604734821
work_keys_str_mv	AT isaacakoto asymptoticresultsformultinomialmodels AT joaotmexia asymptoticresultsformultinomialmodels AT filipejmarques asymptoticresultsformultinomialmodels
_version_	1718410287461171200

Asymptotic Results for Multinomial Models

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